If I had to pick one thing I hate about my 2015 F-150, it's that @#$% auto stop/start. With no way to permanently disable it, I've just gotten into the habit of turning it off every time I start the truck.
Otherwise, I'm in the same boat you are. I'm trying to figure out a way to mount a Tait T-2020 and a Uniden 760XLT around that center console. It's funny, when I was looking at getting it (traded in a leased 2012 F-150), my main concern was mounting the antennas...until I saw that center console. A couple things I'm considering are heavy duty velcro/double sided tape to the passenger side of the console as far forward as I can get them, Another thought is to try and work some wood into the storage track on the side of the console, and mounting to that.